1. Field of the Invention
The present invention relates to a working process end point real time determination method for determining an end point of a working process on a real time basis while the working process is proceeding using a working process measurement signal which exhibits, as the working process proceeds, a great increase or decrease once while including variations and then enters steady state as the working process comes to an end.
2. Description of the Related Art
Some working process apparatus such as a semiconductor process apparatus includes a working process measuring instrument for monitoring the progress of a working process.
One of working process measurement signals obtained from a working process measuring instrument exhibits such a variation with respect to time that it exhibits a great increase or decrease once as a working process proceeds after the lapse of a fixed period of time after the working process is started, and then enters a steady state as the predetermined working process is completed. The steady state in this instance signifies a state wherein the signal exhibits little variation, and more specifically signifies a state wherein the variation amount of the signal per unit time has a very low value close to zero.
The working process measurement signal includes periodical variations because a measurement position is scanned in a fixed cycle or, although the measurement position is fixed, the working process side includes a periodical operation from such a reason that the procedure of the working process involves some irregularity depending upon the spatial position and so forth, and the progress of the working process appears on a signal variation from which the periodical variations are removed. Accordingly, the determination that the working process comes to an end determines a point at which the working process measurement signal completes entrance into a steady state from the condition wherein it includes variations.
Though not particularly shown in the accompanying drawings, in order to determine a process end point from a working process measurement signal which exhibits such a variation as described above, a method is generally used wherein the point of time at which the working process measurement signal exhibits a variation to a value equal to or lower than a predetermined value or a value equal to or higher than a predetermined value is determined as a working process end point.
More particularly, since the working process measurement signal exhibits an increase or a decrease once and then enters a steady state, the working process measurement signal is compared with a predetermined threshold value set in advance, and the point of time at which the working process measurement signal exhibits a change to a value equal to or higher than the threshold value or equal to or lower than the threshold value is determined as a working process end point. The method can be applied to working processing end point determination in a CMP process for performing chemical and mechanical polishing (CMP) of a semiconductor wafer.
FIG. 7 is a cross sectional view showing an example of a semiconductor wafer (hereinafter referred to simply as wafer) which is a working object (polishing object). Referring to FIG. 7, the wafer generally denoted at 1 includes a substrate 4 having a high reflection factor with respect to inspection light, an insulator layer 2 applied to the surface of the substrate 4 and having a low reflection factor with respect to the inspection light or transparent to the inspection light, and a metal layer 3 having a high reflection factor with respect to the inspection light and applied to the entire face of the insulator layer 2 in such a manner that it covers over the insulator layer 2. In a CMP process, the metal layer 3 is polished by a CMP apparatus until the insulator layer 2 is exposed to form metal wiring lines. Accordingly, the point of time at which the metal wiring lines are formed completely is the polishing end point.
An example of an application to such a CMP process as just described is disclosed in Japanese Patent No. 2, 561, 812. The method is illustrated in a flow chart of FIG. 19. Referring to FIG. 19, the working process end point real time determination method illustrated includes a first step A1 and a second step A2. In the first step A1, an average value after each predetermined interval of time of a reflected light amount measured by a polished condition monitoring apparatus of the reflected light amount measurement type is calculated as measured light amount averaged data. Then, in the second step A2, the measured light amount averaged data calculated in the first step A1 is compared with a predetermined threshold value which depends upon the reflection factor of a material formed on the wafer with respect to inspection light and the structure of the wafer such as a pattern density, and the point of time at which the measured light amount averaged data becomes a value lower then the threshold value is determined as the polishing end point.
The measured light amount averaged data calculated in the first step A1 exhibits the following variation with respect to time. In particular, in an initial stage of polishing, since the metal layer 3 having a high reflection factor with respect to the inspection light is applied to the overall area of the uppermost layer of the wafer 1 as seen in FIG. 7, the measured light amount averaged data exhibits a high value. Then, as the polishing proceeds, the metal layer 3 is removed, and the insulator layer 2 having a low reflection factor with respect to the inspection light is exposed and begins to be polished. Or, where the insulator layer 2 is transparent to the inspection light, the inspection light begins to pass through the insulator layer 2 thus exposed and is reflected by the substrate 4 having a low reflection factor. Consequently, the reflected light amount gradually decreases. As the polishing further proceeds, metal wiring lines are finally formed completely. Consequently, even if the polishing thereafter proceeds, the area ratio between the insulator layer 2 and the metal layer 3 does not exhibit a variation any more, and accordingly, the measured light amount averaged data does not vary any more and exhibits a fixed value.
Accordingly, since the point of time at which the metal wiring lines are formed completely is the polishing end point, the point at which the measured light amount averaged data does not exhibit a variation any more but exhibits a fixed value indicates the polishing end point.
The measured light amount averaged data at the point of time of the end of the polishing exhibits the same value for each wafer if the reflection factor of the material formed on the wafer with respect to the inspection light and the structure of the wafer such as the pattern density are the same.
Therefore, in the second step A2, the measured light amount averaged data calculated in the first step A1 is compared with a predetermined threshold value which depends upon the reflection factor of a material formed on the wafer with respect to the inspection light and the structure of the wafer such as a pattern density, and the point of time at which the measured light amount averaged data becomes a value lower then the threshold value is determined as the polishing end point.
However, the conventional method wherein a measured light amount averaged data is compared with a predetermined threshold value to determine a working process end point has a problem in that, where the working process measurement signal exhibits a great variation, the determination of the working process end point cannot be performed with a high degree of accuracy.
Where the variation of the working process measurement signal is great, the working process measurement signal cannot be smoothed sufficiently unless the time interval upon averaging of the signal is sufficiently great. In the conventional method illustrated in FIG. 19, the working process measurement signal cannot be smoothed sufficiently unless the time interval when the reflected light amount is averaged in the first step A1 is great.
However, if the time interval for the averaging is increased, then the measurement signal smoothed data includes a greater amount of influence of data in the past and a delay is produced in the variation of the same. Consequently, a delay is produced in the determination of the working process end point. In this instance, according to the conventional method illustrated in FIG. 19, the determination of the polishing end point is delayed, and this gives rise to excessive polishing.
On the other hand, if the time interval for the averaging is decreased in order to prevent the delay, the variation cannot be smoothed sufficiently, and consequently, the determination accuracy of the working process end point is deteriorated. In this instance, according to the conventional method illustrated in FIG. 19, the determination of the polishing end point is dispersed, which gives rise to shortage of the polishing amount or excessive polishing.
It is an object of the present invention to provide a working process end point real time determination method by which the working process end point can be determined with a high degree of accuracy without an error even if a working process measurement signal has such a great variation that, even if it is smoothed, the variation cannot be removed fully from and still remains in resulting measurement signal smoothed data.
In order to attain the object described above, in a working process end point real time determination method according to a first aspect of the present invention, from a working process measurement signal which indicates the progress of a working process and exhibits a fluctuation, a point of time at which transition of the working process measurement signal into a steady state is completed after the working process measurement signal experiences a great variation once as the working process proceeds is determined on the real time basis while the working process is proceeding.
The working process measurement signal is obtained from a working process measuring instrument and includes a periodical variation because a measurement position is scanned in a fixed cycle or, although the measurement position is fixed, the working process side includes a periodical operation from such a reason that the procedure of the working process involves some irregularity depending upon the spatial position and so forth. Since the progress of the working process appears on a signal variation from which the periodical variation has been removed, in the first step, averaging is performed at intervals equal to an integral number of times the period of the variation to discretely calculate averaged data for each interval equal to the integral number of times the predetermined period.
Because the initial state prior to the working process is not fixed, the working process measurement signal in an initial stage of the working process exhibits a different variation from the procedure of the working process even if the periodical variation is removed from the working process measurement signal in the first step. The variation of the working process measurement signal in an initial stage of the working process is different among different working processes and may sometimes be a very great variation. Therefore, in the second step, end point determination based on the working process measurement signal is not performed for a time which exceeds the time within which such a variation of the working process measurement signal as described above may possibly occur.
Further, in order to cope with a dispersion of the initial variation period of the working process measurement signal which arises from a dispersion of the rate of the working process, in the third step, end point determination based on the working process measurement signal is not performed before the working process measurement signal exhibits a great variation as the working process proceeds, for example, before the working process measurement signal reaches a predetermined value or a predetermined multiple.
Then, determination of the working process end point is performed. However, even if the working process measurement signal is averaged to remove a periodical variation in the first step, the averaged data of the working process measurement signal obtained in the first step still includes remaining noise components originating from irregularity of the working process, the accuracy of a measuring apparatus or mixture of noise. Accordingly, transition of the working process to a steady state cannot be determined from the fact that the gradient (differential value) of the averaged data of the working process measurement signal at the present measurement point of time comes to the proximity of 0, but, for the determination of the working process end point, it is necessary to use data whose noise components have been smoothed sufficiently.
Therefore, in the fourth step, as such smoothing processing, it is possible to calculate an average value of a plurality of ones of the averaged data of the working process measurement signal obtained in the first step which belong to a predetermined period in the past including the value of the averaged data at the present measurement point of time and an average value of another plurality of ones of the averaged data which belong to another predetermined period in the further past and calculate a variation amount between the two average values as an average gradient.
However, if the point of time at which the average gradient obtained in the fourth step comes to the proximity of 0 is detected to determine the working process end point, then since a time delay caused by use of the data in the past is involved in the average gradient, the working process end determination is delayed.
Therefore, in the fifth step, after an absolute value of the average gradient of the averaged data of the working process measurement signal assumes a value equal to or higher than a predetermined value, the average gradient value at the present measurement point of time and another one of the average gradient values in the near past are joined to perform extrapolation to the future to calculate an estimated value of a time at which the average gradient is estimated to become equal to 0 and the working process comes to an end.
In this instance, since the estimated value of the time includes some delay in time caused by use of the data in the past, in the sixth step, the delay time is subtracted from the estimated value up to the end of the working process, and it is temporarily determined that the working process has come to an end if the working process time obtained by the subtraction indicates a time prior to the present measurement point of time.
The estimated value of the time up to the end of the working process includes some error caused by mixture of noise and so forth and the error makes a factor of wrong determination. Therefore, in the seventh step, overlooking some error, a short time gradient of the averaged data of the working process measurement signal is calculated only from the value at the present measurement point of time and the value in the nearest past from within the averaged data of the working process measurement signal calculated in the first step, and it is determined that the working process has come to an end from a logical AND between when the short time gradient reaches a value within a predetermined range successively more than a predetermined number of times, that the short time gradient exhibits a value within the predetermined range totally by more than the predetermined number of times after the absolute value of the average gradient assumes a value equal to or higher than the predetermined value or that the ratio at which the short time gradient assumes a value within the predetermined range is equal to or higher than a predetermined ratio and a result of the determination in the sixth step that a time obtained by subtracting the delay time caused by use of the data in the past from the estimated value up to the end of the working process indicates a time prior to the present measurement point of time.
Where the working process end point real time determination method is applied to a working process with which there is no sufficient time margin in which estimation by extrapolation of a working process end point is to be performed because average data of a working process measurement signal exhibits a sudden variation at the working process end point from a characteristic of a working process object article or a working process apparatus or extrapolation cannot be performed because the manner of the variation with respect to time of the averaged data of the working process measurement signal is different among different working processes, after it is determined that the working process at present is in the proximity of the working process end point from the fact that the absolute value of the average gradient of the averaged data of the working process measurement signal assumes a value equal to or higher than the predetermined value, a short time gradient of the averaged data of the working process measurement signal is calculated only from a value at the present measurement point of time and another value in the nearest past from within the averaged data of the working process measurement signal, and then it is determined that the working process has come to an end if the short time gradient reaches a value within a predetermined range successively more than a predetermined number of times, if the short time gradient exhibits a value within the predetermined range totally by more than the predetermined number of times after the absolute value of the average gradient assumes a value equal to or higher than the predetermined value or if the ratio at which the short time gradient assumes a value within the predetermined range is equal to or higher than a predetermined ratio.
According to a second aspect of the present invention, there is provided a working process end point real time determination method which comprises the first to fourth steps described above and further comprises, next to the fourth step, an eighth step of waiting for an absolute value of the average gradient of the averaged data of the working process measurement signal calculated in the fourth step to become equal to or higher than a first threshold value set in advance, and a ninth step of calculating a short time gradient of the averaged data of the working process measurement signal only from the value at the present measurement point of time and the value in the nearest past of the averaged data of the working process measurement signal calculated in the first step after the absolute value of the average gradient of the averaged data of the working process measurement signal calculated in the fourth step to become equal to or higher than the first threshold value and determining that the working process has come to an end if the short time gradient reaches a value within a second threshold value set in advance successively more than a predetermined number of times, if the short time gradient assumes a value within the second threshold value totally by more than the predetermined number of times after the absolute value of the average gradient becomes equal to or higher than the first threshold value or if the ratio at which the short time gradient assumes a value within the second threshold value is equal to or higher than a predetermined ratio.
According to a third aspect of the present invention, there is provided a working process end point real time determination method which comprises the first to fourth steps described above and further comprises, next to the fourth step, a 23rd step of multiplying a maximum value, a minimum value or an average value of the averaged data obtained for a time between a point of time when a fixed time for excepting a signal variation in an initial stage of the working process elapses and another point of time when the working process measurement signal begins a great variation by different predetermined values to calculate relative values as first and second threshold values, a 24th step of joining the average gradient value at the present measurement point of time and another one of the average gradient values in the near past after a point of time when an absolute value of the average gradient of the averaged data becomes equal to or higher than the first threshold value to perform extrapolation to the future to calculate a time at which the average gradient becomes equal to zero in the future as an estimated value of a working process end time, a 25th step of subtracting a delay time caused by use of the data in the past from the estimated value of the working process end time and temporarily determining that the working process has come to an end if the time obtained by the subtraction indicates a time prior to the present measurement point of time, and a 26th step of calculating a short time gradient of the averaged data only from a value of the averaged data at the present measurement point of time and another value of the averaged data in the nearest past and determining that the working process has come to an end from a logical AND between that the short time gradient assumes a value within the second threshold value successively more than a predetermined number of times, that the short time gradient assumes a value within the second threshold value totally by more than the predetermined number of times after the absolute value of the average gradient assumes a value equal to or higher than the first threshold value or that the ratio at which the short time gradient assumes a value within the second threshold value exceeds a predetermined ratio and the determination result in the 25th step.
The estimated value of the time before the working process end point includes an error originating from noise and so forth mixed thereto, and the error makes a factor of wrong determination. Therefore, in the 26th step, taking it into consideration that some error is involved, a short time gradient of the averaged data of the working process measurement signal is calculated only from a value of the averaged data of the working process measurement signal at the present measurement point of time calculated in the first step and another value of the averaged data in the nearest past, and it is determined that the working process has come to an end from a logical AND between that the short time gradient assumes a value within the second threshold value successively more than a predetermined number of times, that the short time gradient assumes a value within the second threshold value totally by more than the predetermined number of times after the absolute value of the average gradient assumes a value equal to or higher than the first threshold value or that the ratio at which the short time gradient assumes a value within the second threshold value exceeds a predetermined ratio and that the time obtained by subtracting a delay time caused by use of the data in the past from the estimated value of the working process end time is prior to the present measurement point of time.
The first and second threshold values to be used in the 24th and 26th steps are calculated as relative values in the 23rd step by multiplying a maximum value, a minimum value or an average value of the averaged data of the working process measurement signal obtained for a time between a point of time when a fixed time for excepting a signal variation in an initial stage of the working process elapses in the second step and another point of time when the working process measurement signal begins a great variation by different predetermined values.
Since the end point determination based on the working process measurement signal is not performed until the working process measurement signal reaches a predetermined multiple in the third step and besides the threshold values are formed from relative values, even if the magnitude of the working process measurement signal varies generally depending upon a difference in the working object article, the process condition or the measurement condition or the like, the working process end point can be determined correctly.
It is to be noted that, in such a process that the working process measurement signal exhibits little variation in overall magnitude, the threshold values may be formed as fixed values.
When it is determined in the 26th step that the short time gradient exhibits a value within the predetermined threshold value totally by more than the predetermined number of times after the absolute value of the average gradient exhibits a maximum value, if the absolute value of the average gradient assumes a maximum value by a plurality of times before the working process comes to an end, then each time a maximum value is detected, the total number of times is reset to re-start counting.
Where the working process end point real time determination method is applied to a working process with which there is no sufficient time margin in which estimation by extrapolation of a working process end point is to be performed because average data of a working process measurement signal exhibits a sudden variation at the working process end point from a characteristic of a working process object article or a working process apparatus or extrapolation cannot be performed because the manner of the variation with respect to time of the averaged data of the working process measurement signal is different among different working processes, it is first determined that the working process at present is in the proximity of the working process end point from the fact that the absolute value of the average gradient of the averaged data of the working process measurement signal assumes a value equal to or higher than the predetermined threshold value. Then, a short time gradient of the averaged data of the working process measurement signal is calculated only from a value at the present measurement point of time and another value in the nearest past from within the averaged data of the working process measurement signal, and then it is determined that the working process has come to an end if the short time gradient reaches a value within a predetermined threshold value successively more than a predetermined number of times, if the short time gradient exhibits a value within the predetermined range totally by more than the predetermined number of times after the absolute value of the average gradient assumes a value equal to or higher than the predetermined threshold value or if the ratio at which the short time gradient assumes a value within the predetermined threshold value is equal to or higher than a predetermined ratio.
According to a fourth aspect of the present invention, there is provided a working process end point real time determination method which comprises the first to fourth steps and the eighth and ninth steps described above and further comprises, prior to the eighth step, a 23rd step of multiplying a maximum value, a minimum value or an average value of the averaged data obtained for a time between a point of time when a fixed time for excepting a signal variation in an initial stage of the working process elapses and another point of time when the working process measurement signal begins a great variation by different predetermined values to calculate relative values as first and second threshold values.
Each of the working process end point real time determination methods according to the first to fourth aspects of the present invention may be constructed in the following manner.
In the first step of averaging a working process measurement signal at intervals equal to an integral number of times a predetermined period to discretely calculate an average value for each interval equal to the integral number of times the predetermined period as averaged data, the working process measurement signal may be averaged after each time interval within which a working object makes one rotation.
In the first step of averaging a working process measurement signal at intervals equal to an integral number of times a predetermined period to discretely calculate an average value for each interval equal to the integral number of times the predetermined period as averaged data, the working process measurement signal may be averaged after each time interval within which a working object makes an integral number of rotations.
In the first step of averaging a working process measurement signal at intervals equal to an integral number of times a predetermined period to discretely calculate an average value for each interval equal to the integral number of times the predetermined period as averaged data, the averaging of the working process measurement signal only over a predetermined interval of time within a time within which a working object makes one rotation may be performed after each period of rotation of the working object.
In the first step of averaging a working process measurement signal at intervals equal to an integral number of times a predetermined period to discretely calculate an average value for each interval equal to the integral number of times the predetermined period as averaged data, the working process measurement signal may be averaged at time intervals within which inspection light scans a working object.
In the fourth step of calculating an average gradient over a plurality of ones of the averaged data of the working process measurement signal which belong to a predetermined period in the past including the value of the averaged data at the present measurement point of time, an average value of a plurality of ones of the averaged data which-belong to a predetermined period in the past including the value of the averaged data at the present measurement point of time and an average value of another plurality of ones of the averaged data which belong to another predetermined period in the further past may be calculated, and a variation amount per unit time between the two average values may be calculated as the average gradient.
In the fourth step of calculating an average gradient over a plurality of ones of the averaged data of the working process measurement signal which belong to a predetermined period in the past including the value of the averaged data at the present measurement point of time, an expression of a straight line may be determined by a least square approximation method using a plurality of averaged data of a measured light amount which belong to a predetermined period in the past including a value of the measured light amount averaged data at the present measurement point of time, and a gradient of the straight line may be calculated as the average gradient.
In the fifth step of joining the average gradient at the present measurement point of time and another one of the average gradients in the near past to perform extrapolation to the future to calculate an estimated value of time until the working process comes to an end, an expression of a straight line which passes two points of the average gradient of the average gradient data at the present measurement point of time and another average gradient immediately preceding to the same may be determined, and a time at which the average gradient becomes equal to 0 may be calculated from the expression of the straight line only when the gradient of the straight line determined is in the positive if the averaged data exhibits a variation with respect to time wherein the averaged data drops by a great amount once and then enters a steady state or only when the gradient of the straight line determined is in the negative if the averaged data exhibits another variation with respect to time wherein the averaged data rises by a great amount once and then enters a steady state.
In the fifth step of joining the average gradient at the present measurement point of time and another one of the average gradients in the near past to perform extrapolation to the future to calculate an estimated value of time until the working process comes to an end, an expression of a straight line may be determined by a least square approximation method using three or more average gradients of the averaged data which belong to the past including the average gradient of the average gradient data at the present measurement point of time, and a time at which the average gradient becomes equal to 0 may be calculated from the expression of the straight line only when the gradient of the straight line determined is in the positive if the averaged data exhibits a variation with respect to time wherein the averaged data drops by a great amount once and then enters a steady state or only when the gradient of the straight line determined is in the negative if the averaged data exhibits another variation with respect to time wherein the averaged data rises by a great amount once and then enters a steady state.
An average gradient in a short time including a comparatively small number of averaged data in the past may be calculated and the number of times by which the average gradient in the short time assumes a value equal to or greater than 0 may be counted, and it may be determined that the working end point comes if the end point determination time calculated by such a method as described above is smaller than the present working time and the count number by which the relationship that the average gradient in the short time is equal to or greater than 0 is satisfied is equal to or greater than a predetermined number.
A predetermined time which exceeds a time within which a great variation of the averaged data in an initial stage of the working occurs may be set in advance, and the predetermined time and the working elapsed time till the present may be compared with each other and then the working end point determination operation is not performed until the present working elapsed time becomes equal to or greater than the predetermined time set in advance.
A maximum value of the averaged data till the present measurement point of time may be determined, and the working end point determination operation is not performed until it is determined, when the averaged data drops by a predetermined ratio from the maximum value, that a drop of the averaged data which is a characteristic of the averaged data in the proximity of the working end point has started.
When the end point determination time is to be calculated, a time obtained by adding or subtracting a predetermined time to or from a working time till the present since the oldest point of time in the past used for the calculation of the average gradient may be subtracted from a time at which the average gradient assumes a value equal to 0 to calculate the end point determination time thereby to delay or advance the determination of the working end point by a predetermined time.
Preferably, the threshold values are calculated as relative values by multiplying a maximum value, a minimum value or an average value of the averaged data of the working process measurement signal obtained for a time between a point of time when a fixed time for excepting a signal variation in an initial stage of the working process elapses and another point of time when the working process measurement signal begins a great variation by different predetermined values.
Since the threshold values are formed from relative values, even if the magnitude of the working process measurement signal is varied generally by a difference in a working object, a process condition, a measurement condition or the like, the effect that determination of the working process end point can be performed appropriately can be achieved.
Preferably, when it is determined that the short time gradient exhibits a value within the predetermined threshold value totally by more than the predetermined number of times after the absolute value of the average gradient exhibits a maximum value, in such a process that the absolute value of the average gradient assumes a maximum value by a plurality of times before the working process comes to an end, each time a maximum value is detected, the total number of times is reset to re-start counting.
Where the present invention is applied to a CMP apparatus which performs chemical and mechanical polishing of a semiconductor wafer, since the working object is a wafer, the working process end point real time determination method is preferably constructed in the following manner.
In particular, the working process end point real time determination method comprises a tenth step of calculating, as measured light amount averaged data, an average value after each predetermined interval of time of a reflected light amount measured by a polished condition monitoring apparatus of the reflected light amount measurement type mounted on the CMP apparatus for irradiating inspection light upon a polished face of the semiconductor wafer and monitoring a polished condition from a variation of the reflected light amount obtained then, an eleventh step of calculating, as average gradient data, an average rate of change over a plurality of measured light amount averaged data which belong to a predetermined period in the past including the value at the present measurement point of time of the measured light amount averaged data calculated in the tenth step, a twelfth step of joining, after an absolute value of the average gradient of the measured light amount averaged data calculated in the eleventh step assumes a value equal to or higher than a predetermined value, the average gradient at the present measurement point of time and another one of the average gradients in the near past to perform extrapolation to the future to estimate and calculate a time at which the relationship that the average gradient is equal to 0 is reached, a thirteenth step of subtracting a polishing time till the present since the oldest point of time in the past used for calculation of the average gradient in the eleventh step from the time at which the relationship that the average gradient is equal to 0 is reached to calculate an end point determination time, and a fourteenth step of comparing the end point determination time calculated in the thirteenth step and the present polishing time with each other and determining a point of time at which the end point determination time becomes equal to or smaller than the present polishing time as a polishing end point.
Alternatively, the working process end point real time determination method may comprise a tenth step of calculating, as measured light amount averaged data, an average value after each predetermined interval of time of a reflected light amount measured by a polished condition monitoring apparatus mounted on a CMP apparatus for performing chemical and mechanical polishing of a semiconductor wafer, an eleventh step of calculating, as average gradient data, an average rate of change over a plurality of measured light amount averaged data which belong to a predetermined period in the past including the value at the present measurement point of time of the measured light amount averaged data calculated in the tenth step, a twelfth step of joining, after an absolute value of the average gradient of the measured light amount averaged data calculated in the eleventh step assumes a value equal to or higher than a predetermined value, the average gradient at the present measurement point of time and another one of the average gradients in the near past to perform extrapolation to the future to estimate and calculate a time at which the relationship that the average gradient is equal to 0 is reached, a thirteenth step of subtracting a polishing time till the present since the oldest point of time in the past used for calculation of the average gradient in the eleventh step from the time at which the relationship that the average gradient is equal to 0 is reached to calculate an end point determination time, a 31st step of multiplying a maximum value or an average value of the measured light amount averaged data obtained for a time after a fixed time for excepting a signal variation in an initial stage of the polishing elapses until the measured light amount averaged data begins to drop a great amount by a predetermined value to calculate a relative value as a threshold value, a 32nd step of calculating a first average value of a plurality of ones of the measured light amount averaged data which belong to a predetermined period in the past including the value of the measured light amount averaged data at the present measurement point of time and a second average value of another plurality of ones of the measured light amount averaged data which belong to another predetermined period in the further past and calculating a variation amount per unit time between the first and second average values as an average gradient in a short time, a 33rd step of detecting that the average gradient data calculated in the eleventh step assumes a minimum value, a 34th step of counting an accumulated value of the number of times by which the average gradient data in the short time calculated in the 32nd step assumes a value equal to or higher than the counter threshold value after it is determined that the average gradient data calculated in the eleventh step assumes a minimum value, a 35th step of resetting, if the average gradient data calculated in the eleventh step assumes a maximum value after it is determined in the 33rd step that the average gradient data assumes a minimum value, the accumulated value counted in the 34th step and repeating the minimum value detection in the 33rd step, and a 36th step of comparing the end point determination time and the present polishing time with each other and determining that the polishing end time comes if the end point determination time is equal to or smaller than the present polishing time and the number of times by which the average gradient in the short time counted becomes within the predetermined threshold value is equal to or greater than a predetermined number.
With any of the working process end point real time determination methods according to the present invention, a working process end point is estimated by extrapolation from a manner of the variation of the average gradient of the averaged data in a predetermined period of the working process measurement signal to perform determination of the end point, or where the working process does not allow such extrapolation, it is first determined that the working process at present is in the proximity of the working process end point based on the absolute value of the average gradient of the averaged data of the working process measurement signal, and then the working process end point is determined using a gradient in a short time calculated only from a value at the present measurement point of time and another value in the nearest past from within the averaged data of the working process measurement signal. Consequently, even when the working process measurement signal exhibits such a great variation that, even if it is averaged, a variation remains in the averaged working process measurement signal data, the effect that determination of the working process end point can be performed appropriately with a high degree of accuracy without suffering from wrong determination can be achieved.
The above and other objects, features and advantages of the present invention will become apparent from the following description and the appended claims, taken in conjunction with the accompanying drawings in which like parts or elements are denoted by like reference symbols.